Lighting move with object movement
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You'll want to use something known as Parenting to do this. Joining only works if the objects are the same type, and only on certain types of objects, for example meshes.

To use parenting, select the object that you want to be the follower, and then the object that you want it to follow. Press Ctrl+P and choose "Object". Now the follower (child) will be joined to the parent object and follow wherever it moves. You can still move the child object independently as well.